Feb., 1949
739
NOTES A Method of Estimating and Minimizing the Error of Measurement of the Rate of a Radioactive Exchange Reaction BY NORMAN DAVIDSON A N D JOHN H . SULLIVAN It has been explicitly pointed out by several authors that for a radio-active exchange reaction between two components in chemical equilibrium, the activity of either component varies in a simple exponential manner with time.'I2 We present here, as a consequence of this analysis, a method for: (a) the estimation of the error, due to the error of radioassay, in the rate constant for the exchange reaction, as a function of the extent of exchange; (b) the selection of the optimum degree of exchange to minimize this error.a For the case where the rate is measured by the decrease in the activity of the component that initially contained all the activity, the integrated rate expression is In
[(g + 1): - i] = -R(a,b) a +abb t
(1)
I n this relation: a is concentration of component A that initially contained all the activity; b is concentration of initially inactive .component B ; tis initial activity of A; x is activity of A a t time t and R(a, b) is the rate of exchange. For very short times of reaction x will be almost the same as G and the error in the rate large. For long times of reaction, the components will be almost in equilibrium with respect to the distribution of activity which will then change but little with time. It is often the case that the errors in a, b, t are small compared t o the errors of radioassay in x and c. Set z = x/c and s = R((a b)/ ab)t. The variable s is dimensionless and proportional t o two factors: (1) Rt, the total number of concentration units (i. e., atoms/cc. or moles/liter) that have undergone mutual exchange, and (2) the term (a b)/ab. (Displayed in the form s = R t / b Rt/a, it is evident that s is the sum of the number of exchanges per atom of a, and the number of exchanges per atom of b). Then
+
+
+
The relation us = Ids/dzlu, holds for the standard deviations, us and u., of s and z, because of the assumption that the error in s is due entirely to the error in z.( Then (1) McKay, Nature, 142, 997 (1938). (2) Du5eld and Calvin, Tsra JOURNAL, 68, 557 (1945). (3) Roseveare, ibid., 68,1651 (1931),has applied similar arguments to the problem of estimating and minimizing the error in the rate constants for chemical reactions. (4) See, for example, Margenau and Murphy, "The Mathematics of Phyiicll End Chemistry," D. Van Nostrand Co., New York, N. Y., 1048. p. 4oa
+
For U ~ , ( U , / ~ = ) ~(U~/X)~ ( U ~ / C ) ~ the ; standard deviations of the activities may be due to statistical counting errors or may be manipulative errors determined by reproducibility tests. It is often the case that the fractional error in x,(u,/x), is a constant; this is roughly true, for example, if the error is principally a counting error and one counts all samples to the same number of counts, or if the error is a manipulative error in preparing chemically identical samples for radioassay. For such cases, the minimum of E locates the point for minimum error in s (and hence in the rate function R). Knowing the value of s corresponding to the minimum value of E and using a preliminary value of R, the optimum t may be chosen. 14 12 I. I I
10
'_
.^
6
h
L? a
8
q'
4
2
I
I
1
I
I
3
I
I
5
S.
Fig. 1.-Error
functions for exchange reactions.
The minimum of the error function, E , may be found by solution of the equation: s - 1 = (b/a) exp( -s). I t will generally be more useful to construct a family of curves like those in the figure so that the error in s will be known for any s (or z). Estimates of the standard deviation in s obtained in this way are useful, for example as weighting factors in averaging data or in least squares treatments of data on the variation of rate of exchange with temperature or ionic strength. For such applications, the function E is useful even when the fractional error of radioassay is not constant. For these cases, knowing ux as a function of x and hence (for given a and b) as a function of s, one could construct the function, E(s)u,(s)/ x ( s ) , and thus select the point of minimum error. For the usual case where U,/X does not change too rapidly with x,i t may be sufficient to select by inspection a point in the region of the minimum of the E ( s ) curve without making the more elaborate calculations required to select the optimum point.
Vol. 71
NOTES
740
For the case where the rate of exchange is measured by the growth of activity, y, in B ~ ( =0 Y (-1 [1 - exp (-41 (4) d In s/d In ( y / y ( m ) ) = (exp(s)
- l ) / s = F(s)
(5)
The figure contains a plot of this function, too. I n this case, of course, the fractional error in y cannot possibly be constant as y approaches zero; a n estimate of uy as a function of y is needed for selecting an optimum reaction time or calculating the error of a particular determination. CONTRI~UTION No. 1233 FROM THB GATESAND CRELLINLABORATORIES OF CHEMISTRY CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA 4, CALIFORNIA RECEIVED AUGUST9, 1948
A Convenient Synthesis of N,N-Dimethyl-pnitroaniline and N,N-Dimethyl-o-nitroaniline BY TODW. CAMPBELL
There are a number of methods in the literature for the preparation of N,N-dimethylnitroanilinel; but most of them are troublesome and result in low yields of a product which is usually of not too high purity. The methods in the literaturelg,' which give acceptable or good yields involve a reaction in which a nitrohalobenzene is allowed to react with dimethylamine. The author has found that this reaction is most conveniently brought about by refluxing a pyridine solution of nitrohalobenzene with a mixture of dimethylamine hydrochloride and sodium bicarbonate. The desired product is obtained in virtually quantitative yield; in the case of the para isomer, the product can be crystallized directly from the reaction solvent in a high state of purity. This procedure is therefore recommended for the preparation of these two substances. Experimental Part 9-Nitrodimethylanilie.-A mixture of 42 g. of #-bromonitrobenzene, 300 cc. of pyridine, and 50 g. of sodium
melting point to 163.5-164'. The over-all yield of pure product was 32.4-33.6 g. (94-97y0). o-Nitrodimethylanilme.-The above procedure was employed to prepare the ortho substituted derivative. Ten grams of o-nitrochlorobenzene gave 8.9 g. (85%) of product; b . p . 149at20mm.; n2%1.6080. Anal. Calcd. for CsHloNzOz; C, 57.81; H, 6.06. Found: C, 57.53; H, 6.21. UNIVERSITY OF CALIFORNIA Los ANGELES24, CALIF. RECEIVED AUGUST19, 1948
Vapor Density of Diboranel BY E. M. CARR,J. T. CLARKE AND H. L. JOHNSTON
I n connection with the process of adding diborane to a calorimeter i t was necessary to determine its density a t 275.16'K. The diborane was obtained from the Naval Research Laboratory, subjected to a two-plate distillation and shown by the cryoscopic method to have a purity of 99.95 mole per cent. The diborane was introduced into an evacuated, weighed and calibrated 1-liter Pyrex bulb immersed in a constant temperature waterbath a t 275.16'K. and constant to 0.01' C. during the measurement. The pressure was read on a 15 mm. i. d. manometer using a Gaertner cathetometer and a standard meter bar in an insulated case; the readings were converted to standard conditions and meniscus corrections made according to Cawood and Patterson.2 The bulb was then reweighed (using a similar bulb as tare) on a Troemner 4-kg. balgnce. One bulb had '/* inch Pyrex helices with a surface area 16.0 times that of the interior part of the bulb added to it. Since all density measurements were made a t approxi-, mately atmospheric pressure the amount of adsorption was assumed to be constant. The results were used to calculate the density and the second virial coefficient B in the equation
bicarbonate was placed in a 500-cc. round-bottom flask. To this mixture was added 30 g. of dimethylamine hydrochloride dissolved in about LO cc. of warm water. The mixture was refluxed for ten hours. Mechanical stirring was not employed, since serious bumping did not occur. At the end of the reflux period, the hot solution was filtered free of inorganic salts, and the latter was extracted with 200 cc. of acetone, which was added to the pyridine solution. The mixed extracts were boiled, and water added to near the cloud point. On cooling, bright yellow needles of +-nitrodimethylanilhe, 1-3 cm. in length, crystallized out. The melting point was observed to be 163.7-164.1' (lit. 163-166") on a calibrated Anschiitz thermometer in a Hershberg apparatus. The mother liquor on concentration to one third of its original volume gave an additional small yield of fine yellow needles, which had a melting point anywhere from 1-10 degrees low, for various experiments. One recrystallization from methanol raised the
0.98832 .98201 .99445 .94553 .96219 .97098
(1) (a) Beilstein "Handbuch," Vol. XII, 690, 714, and first Supplement; (b) Le Fevre, J . Chcm. Soc., 147 (1930); (c) Davies, Bull. soc. chim., [SI 9, 295 (1935); (d) Donald and Reade, J Chcm. SOC.,53 (1935); (e) Marsden and Sutton, ibid.. 599 (1936); (f) Shorygin, Topchier and Anan'ina, J . Gen. Chcm. (U.S. S. R . ) , 8,981 (1938); ( g ) Hodgson and Kershaw, J . Chcm. Soc., 280 (1930); (h) Evans and Willisma, ibid., 1199 (1939); (i) Senear, Rapport, Mead, Maynard and Koapfli, J . Or& Chcm., 11, 378 (1946).
(1) This work was carried out under contract between the Office of Naval Research and The Ohio State University Research Poundation. (2) Cawood and Patterson, Trans. Faraday Soc.. 19, 514-523 (1933).
where A equals moles of diborane adsorbed on the surface of a 1-liter bulb and was found to have a value of 2.4 X mole. A summary of the data is Pressure, atm.,
P
Temperature, OK.,
T
Moles in gas phase, n - A
Volume of bulb, ml.,
V
275:20 0.048232 1090.2 275.14 .047296 1076.4 275.16 ,048488 1090.2 ,046104 1090.2 275.16 275.17 .046314 1076.4 275.15 ,046690 1076.4 Average Av. deviation
Second virial coef. B (ml.) 275.16' K.
1 atm. 275.16'K.
-247 -233 -223 -234 -227 -199 -227 *11
1.2398 1.2393 1.2386 1.2393 1.2388 1.2374 1.2389 *0.0006
Density
&/I.
NOTES
Feb., 1949 The value B equals -227, determined experimentally agrees very well with the value B equals - 240 calculated from Berthelot's equation and the critical constants of A. E. N e ~ k i r k . ~ (3) A. E. Newkirk, THISJOURNAL, 70, 1978 (1948).
THECRYOGENIC LABORATORY DEPARTMENT O F CHEMISTRY THEOHIOSTATEUNIVERSITY RECEIVED SEPTEMBER 13, 1948
74 1
tracted with 100 rnl. of water; the combined supernatant fluids were filtered and acidified with acetic acid. The yellow-orange xanthopterin precipitate was collected by centrifugation, washed seven times with water, then with alcohol, finally with ether and dried in vacuo. The yield was 1.95 g. of xanthopterin monohydrate (79%). At p H 11.0 the monohydrate has an Bi?m. of 0.92 a t 255 mp and 0.355 a t 390 mfi.
Microbiological
Each compound was tested for its ability to serve as a substitute for adenine in the growth of Lactobacillus casei with thymine as nutrilite a t a The Preparation of Xanthopterin concentration of 10 y per ml.' It will be seen BY GERTRUDE €3. ELION,AMOSE. LIGHTAND GEORGEH. (Table I) that whereas pure xanthopterin (Expt. HITCHINGS 1) and dihydroxanthopterin (Expt. 5 ) have only The method of Totter' for the preparation of inhibitory effects, the product of the complete xanthopterin (2-amino-4,6-dihydroxypteridine) Totter procedure (Expt. 2) the product of further has several advantages with respect to the time purifications of this material (Expt. 3) and that obinvolved, convenience and availability of starting tained by the oxidation of pure dihydroxanthopmaterials, over those of P ~ r r r n a n nand ~ ~ ~Kos- terin by silver oxide (Expt. 4) all possess purine~ h a r a .As ~ will be shown, however, the product of like activity. This activity is not due to the startthis procedure is impure, as determined spectro- ing material (Expt. s), the intermediate oxalyl graphically. Moreover, such impure xanthopterin derivative (Expt. 7) or leucopterin (Expt. 8). is shown to have a microbiological activity quite The activities appear to be properties of by-proddifferent from that of pure xanthopterin. The pos- ucts which are formed in the various steps and in sibility exists that some of the reported biological some instances deposit slowly on stavding of the activities of xanthopterin may be attributable to solutions (Expt. 9, Expt. 10). This finding demsuch impurities. This note describes modifica- onstrates the necessity for the isolation and purifitions of the Totter procedure which result in their cation of the intermediates as a requisite for the climination. preparation of pure xanthopterin. Experimental : Preparation of Xanthopterin Leucopterin.-The leucopterin was prepared by the method of P ~ r r m a n n . ~On standing, after neutralization, the acid filtrate from the crystallization of leucopterin deposited a red precipitate which had microbiological activity (Precipitate A, Erpt. 9, Table I ) . Dihydroxanth0pterin.-Leucopterin (6 g., 0.03 mole) was suspended in 40 ml. of water and 4% sodium amalgam (88 g., 0.153 mole) was added in small portions with stkring, the temperature being maintained below about 50 On completion of the reduction the mixture was decanted from the mercury and chilled in an ice-bath. The sodium salt of dihydroxanthopterin precipitated in shiny crystals which were filtered off, washed with 5 ml. of ice water and dried in vucuo (3.73 g., 60%). A small additional quantity of dihydroxanthopterin (0.46 g.) was obtained by acidification of the niother liquors. The filtrate from this fraction, on standing several days, deposited a red precipitate which had purine-like activity (Precipitate B, Expt. 10, Table I ) . The sodiuni dihydroxanthopterin (3.73 9.) was dissolved in 300 ml. of hot water, with the aid of a small quantity of sodium hydroxide solution, filtered and acidified with acetic acid. Dihydroxanthopterin monohydrate precipitated as pale yellow microcrystals (3.4g.); cf. Hitchings and Elion .6 Xanthopterin.-Dihydroxanthopterin monohydrate (2.5 g., 0.0125 mole) was dissolved a t room temperature in 200 ml. of water containing 1.4 g. of potassium hydroxide. Potassium permanganate solution (84 ml. of 0.01 M ) was added dropwise over the course of ten minutes. After coagulation of the manganese dioxide, the solution was separated by centrifugation. The manganese dioxide was ex-
.
(1) Totter, J . B i d . Chem., 164, 105 (1944). (2) Purrmann, Ann., 546, 98 (1940). (3) Purrmann, ibid., 648, 284 (1941). (4) Koschara, Z . physiol. Chcm., 277, 159 (1943). (5) Purrmann. Ann., 644, 182 (1940). (6) Hitchings and Elion, THIS JOURNAL, 71, 467 (1949).
TABLE I PURINE-LIKEACTIVITYOF XANTHOPTERIN AKD INTERMEDIATES
Expt.
Compound
Titer With compound 1 mg. per Con10 ml. trol
1 Xanthopterin I" 0.4 1.1 2 Xanthopterin 11' 2 5: 1.1 3 Xanthopterin 111" 2.25 1.0 4 Xanthopterin IVd 1.9 1.3 5 Dihydroxanthopterin 0.3 0.6 6 2,4,5Triamino-6-hydroxy0.5 0.5 pyrimidine 7 2,4-Diamino-6-hydroxy-5-oxal- 0.8 1.1 amidopyrimidine 8 Leucopterin 0.4 0.6 9 Precipitate A 3.7 1.2 10 Precipitate B 5.0 1.2 11 Adenine sulfate (0.1 mg.) 7.1 1.2 a Permanganate oxidation of purified dihydroxanthopterin. * Silver oxide oxidation of crude dihydroxanthopterin. Purified sample of II.* Silver oxide oxidation of purified dihydroxanthopterin. THEWELLCOME RESEARCH LABORATORIES TUCKAHOE 7, NEW YORK RECEIVED JUNE 1, 1948 (7) Hitchings, Falco and Sherwood, Science, 102, 251 (1945). (8) Crude xanthopterin prepared by Totter's method was dissolved in N sulfuric acid, treated with norite and filtered. The product was precipitated with ammonium hydroxide, washed, dried, rewashed and redried. This treatment increased the at 390 mp in glycine buffer of pH 11.0 from a value of 0.31 to 0.35,the latter indicating approximate purity. The greater part of the microbiological activity remained, however.
742
NOTES
Absorption Spectra of Some Benzal and Mesitylal Schiff Bases BY LLOYDN. FERGUSON AND JOHN K. ROBINSON
When considering the relative light absorptions of two compounds such as
Vol. 71
does not affect appreciably the molecular extinction. The only explanation offered a t this time for the trend in the differences of Xmax. is to say that forms such as
/CHs CI)-CH=N
and H a C a - C H = N
\X
\X \CHI
where X is any simple group, it is difficult to predict whether the steric effect of the ortho methyl groups in the mesityl compound will decrease absorption from that of the simple phenyl compound or whether there will be an increase in absorption due to hyperconjugation of the methyl groups. For this reason, the spectra of several Schiff bases of benzaldehyde and mesitylaldehyde were measured. The spectral characteristics are listed in Table I. TABLE I SPECTRAL CHARACTERISTICS OF SOMEBENZAL A N D MESITYLAL SCHIFFBASES Oxime
Compound
(mr)
Benzal Mesitylal Difference
252 252 0
9-Nitrophenylhydrazone Xrn
Xm em
(mr)
14,300 407 9,400 411 4,900 4
Ethylenediamine
contribute t o the resonances of benzaldoxime and benzal-p-nitrophenylhydrazone. Such forms would be opposed by the hyperconjugation of the methyl groups in the mesityl nucleus. I t may be that the two effects just cancel one another in the mesitylaldoxime, that the hyperconjugation is slightly more effective than the opposing resonance in the mesitylal-p-nitrophenylhydrazone and that in the ethylenediamine compounds, where the corresponding resonant forms cannot exist and the chromophoric system is double, the hyperconjugation causes a much larger bathochromic effect. DEPARTMENT O F CHEMISTRY HOWARD UNIVERSITY WASHINGTON, D. C. RECEIVED OCTOBER 9, 1948
Xm
em
(mr)
em
34,200 247l 29,000' 31,700 264 8,100 2,500 17 20,900
From these results, i t is observed that there are no significant differences between the wave lengths of maximum absorption of the two oximes or of the two p-nitrophenylhydrazones. In going from dibenzalethylenediamine to dimesitylalethylenediamine there is a bathochromic effect. This, perhaps, is due to the hyperconjugation of the methyl groups becoming more prominent since the chromophoric system is double. Actually upon constructing the Fisher-Hirschfelder models of these three classes of compounds there appears to be only a small steric hindrance between the mesityl methyl groups and the group X.2 It has been observed before3 that small steric hindrances have little effect upon Amax. but do decrease emax..This is illustrated in the present case by the oximes and the ethylenediamines. It is noted that this effect is very small in the case of the nitrophenylhydrazones ; however, this is understandable. The nitrophenylhydrazones have absorption bands near 400 mu4 without the aid of the phenyl or mesityl groups a t the other end of the molecule, and consequently steric hindrance (1) Taken from Ferguson and Branch, THIS JOURNAL, 66, 1467 (1944). (2) O'Shaughnessy and Rodebush found the steric interference between the ortho methyl groups and the carbonyl oxygen of 2,4,6trimethylacetophenone to be hardly strong enough to prevent a coplanar configuration, ibid., 62, 2910 (1940). (3) O'Shaughnessy and Rodebush, i b i d . , 62, 2910 (1940). (4) Ferguson and Battle, Report presented before the Organic Division of the Washington Chemical Society, Oct., 1948, at Washington, D. C.
Comparison of Age with the Relative Abundance of Argon and Potassium in Rocks BY R. L. FARRAR, JR.,
AND
GEORGE H. CADY
The study reported in this communication was done as a test of the proposal of Thompson and Rowlands' that the accumulation of argon resulting from decay by K electron capture of K40 should serve as a measure of the age of rocks containing potassium. For this study solid rocks of known geologic age were kindly furnished by G. E. Goodspeed of our Department of Geology. The analytical procedure involved the following steps : (1) A 60-g. sample of sodium carbonate was freed of argon by pumping away gas for three hours from the molten salt held in a stainless steel vessel a t about 950". (2) Argon and other gases were removed from the surface of a 10-g. sample of rock composed of pea-sized pieces by allowing the material to stand for about an hour a t room temperature in a vacuum. (3) The rock was then dissolved in the sodium carbonate a t 950 t o 1000". This process was allowed to continue for a twenty-four-hour period t o seNe and cure complete liberation of rare gases. (4) He A Kr Xe were determined in the gas, using methods previously described by Cady and Cady.z Since spectroscopic tests showed that not more than traces of Ne, Kr or Xe could have been present in each case, the results of the analyses are reported in the table as helium and argon, respectively. ( 5 ) Potassium was determined in the mass resulting from the sodium carbonate fusion.
+
+
+
Conclusions: (1) These analyses indicate no regular increase of the A/K ratio with age. (2) The range in argon content is much less than that of helium. (3) Most of the argon in a t least the first two samples probably originated from a source, perhaps the atmosphere, other than the (1) F. C. Thompson and S. Rowlands, Nature, 161, 103 (1943). (2) G.H.Cady and H. P. Cady, Ind. Eng. Chcm.. Anal. Ed., 17, 760 (1945).
NOTES
Feb., 1949
743
TABLE I COMPARISON O F AGEWITH Description of sample
Quartz, Cornucopia formation Soda feldspar
Location from which obtained
Cornucopia, N. E. Oregon
Ohanepecosh Hot Springs, Washington Potash feldspar, Cornucopia, N. E. Oregon Cornucopia formation Bostonite Marblehead, Massachusetts Granite, Silver Silver Plume, Colorado Plume Formation Granite Sudbury, Ont. Granite gneiss
Sudbury, Ont.
THE He cc./g.'at S. T.P.
RATIOA/K
IN
A cc./gI a t S. T.P.
ROCKS K, %
G. ats, A G. ats. K
Approximate age in millions of years
0,027 8.4 x 10-4 10-4
0.43
0.19 X lo-*
3.25 X lo-'
12.8
lo-'
0.81 X lo-'
2.08
1.4 X
1.91
100 (Late Mesozoic) 7 . 7 x IO-' 30 (Tertiary) 4.4 x lo-' 100 (Late Mesozoic) 300 6 . 8 X 10-8 (Carboniferous) 1.3 X 10-6 9403
10-4
3.33
2.4
5 . 2 X IO-'
1.05
8 . 6 X 10-6
0,022 X 0.062
x
